Question

for a sample of 120 transformers built for heavy - industry, the mean and standard deviation of the number of sags per weeks were 178 and 18, respectively. also, the mean and standard deviation of the number of swells per week were 327 and 22, respectively. consider a transformer that has 362 sags and 116 swells in a week. a. would you consider 362 sags per week unusual, statistically? explain. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. yes. the z - score is , meaning that this is an outlier and almost every other transformer has fewer sags. (round to two decimal places as needed.) b. no. the z - score is , meaning that the number of sags is not unusual and is not an outlier. (round to two decimal places as needed.) c. no. the z - score is , meaning that less than approximately 68% of transformers have a number of sags closer to the mean. (round to two decimal places as needed.) d. yes. the z - score is , meaning that this is an outlier and almost every other transformer has more sags. (round to two decimal places as needed.) e. this cannot be determined, since the iqr is not provided and cannot be found from the provided information.

Explanation:

Step1: Recall z - score and outlier concept

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. A z - score with $|z|> 2$ is often considered an outlier.

Step2: Calculate the z - score for the given value

Let $\mu = 327$, $\sigma=22$, and $x = 362$. Then $z=\frac{362 - 327}{22}=\frac{35}{22}\approx1.59$. Since $|1.59|<2$, the value is not an outlier.

Answer:

B. No. The z - score is 1.59, meaning that the number of sags is not unusual and is not an outlier.